The intelligence quotient (iq) test scores for adults are normally distributed with a mean of 100 and a standard deviation of 15. what is the probability we could select a sample of 50 adults and find that the mean of this sample is between 98 and 103?
What is the maximum value of y = cos (θ) for values of θ between −720° and 720°?
Answer:
B. 1
Step-by-step explanation:
just got it right on edge
The maximum value of y = cos(θ) for values of θ between -720° and 720° is 1.
The cosine function has a maximum value of 1 when the angle is 0 degrees or 360 degrees (or any integer multiple of 360 degrees).
In the given range of θ between -720° and 720°,
It can be seen that -720° and 720° are integer multiples of 360 degrees.
Therefore, the maximum value of y = cos(θ) for values of θ between -720° and 720° is 1.
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Show how to multiply 6 x 298 using friendly numbers and then use properties and mental math.
Stefan is conducting an experiment to find the level of pollution in the air. He found that there are about 3 billion dust particles in one square meter of space. What is the approximate weight of 3 billion dust particles, if one dust particle weighs 4.66 × 10-12 grams? 1.4 × 10-4 grams
In a suvey of 100 out-patients who reported at a hospital one day it was find out that 70 complained of fever, 50 complained of stomachs and 30 were injured. All 100 patients had at least one of the complains. How many patients had all three complains?
Final answer:
To find the number of patients who had all three complaints (fever, stomach issues, and injury), we can use a Venn diagram. From the given information, we determine that 30 patients had all three complaints.
Explanation:
To find the number of patients who had all three complaints, we can use a Venn diagram. Let's start with the information given:
Total number of patients = 100Number of patients who complained of fever = 70Number of patients who complained of stomach issues = 50Number of patients who were injured = 30All 100 patients had at least one complaintTo determine the number of patients who had all three complaints, we need to find the overlapping region in the Venn diagram. From the given information, we can determine the following:
The number of patients who complained of fever and stomach issues = 100 - 30 (injured patients) = 70The number of patients who complained of fever and were injured = 70 - 50 (patients with stomach issues) = 20The number of patients who complained of stomach issues and were injured = 50 - 20 (patients with both fever and injury) = 30The number of patients who had all three complaints = 30 (those who complained of stomach issues and were injured)Therefore, the number of patients who had all three complaints is 30.
Final answer:
To find out how many patients had all three complaints of fever, stomach pain, and injury, we used the principle of inclusion-exclusion and found that 25 patients had all three complaints.
Explanation:
To determine how many patients had all three complaints (fever, stomach pain, and injury) at the hospital, we can use the principle of inclusion-exclusion from combinatorics.
First, we add the number of people with each complaint:
People with fever: 70
People with stomach pain: 50
People with injury: 30
According to the inclusion-exclusion principle:
Total with all complaints = (People with fever) + (People with stomach pain) + (People with injury) - (People with fever and stomach pain) - (People with fever and injury) - (People with stomach pain and injury) + (People with all three complaints)
Since all 100 patients had at least one complaint, and assuming the least number of people with multiple complaints, we minimize the terms (People with fever and stomach pain), (People with fever and injury), and (People with stomach pain and injury). The minimum number for all these combined categories is the sum of individual complaints minus the total number of patients, which is (70 + 50 + 30) - 100 = 50.
Therefore, if there were no people with all three complaints, the total with any two complaints would be 50. However, this number includes people with all three complaints three times (once for each pair of complaints). To correct this, we subtract twice the number of people with all three complaints to get the true number of people with exactly two complaints:
50 - 2*(People with all three complaints) = Total with exactly two complaints
If there are no people with exactly two complaints, then this means that all 50 are those with all three complaints:
50 - 2*(People with all three complaints) = 0
Solving for (People with all three complaints), we get:
(People with all three complaints) = 50 / 2
(People with all three complaints) = 25
This result suggests that 25 patients had all three complaints of fever, stomach pain, and injury.
Francisco has a savings account balance of 2,033.88. The interest rate on the account is 2.9% compounded monthly. If he opened the account nine years ago what was the value of his initial deposit.
To find the initial deposit (P) of Francisco's savings account, we can use the compound interest formula P = A / (1 + r/n)^(nt) with the given values, leading to P = 2,033.88 / (1 + 0.029/12)^(12*9) and solve for P.
Explanation:To determine the value of Francisco's initial deposit in a savings account that has grown to $2,033.88 with an interest rate of 2.9% compounded monthly after nine years, we need to use the formula for compound interest:
P = A / (1 + r/n)^(nt)
Where:
P is the principal amount (initial deposit)A is the amount of money accumulated after n years, including interest.r is the annual interest rate (decimal)n is the number of times that interest is compounded per yeart is the time in yearsGiven:
A = $2,033.88r = 2.9% or 0.029n = 12 (since the interest is compounded monthly)t = 9 yearsSubstituting the given values into the formula, we get:
P = 2,033.88 / (1 + 0.029/12)^(12*9)
After calculating the above expression, we can find the initial deposit Francisco made into his savings account nine years ago.
Final answer:
Francisco initially deposited approximately $1,511.29 into the savings account.
Explanation:
To find out how much money Francisco initially deposited, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount ($2,033.88)
P is the principal (initial deposit)
r is the interest rate per period (2.9% or 0.029 in decimal form)
n is the number of compounding periods per year (12 for monthly compounding)
t is the number of years (9)
Plugging in the values, we can solve for P:
2,033.88 = P(1 + 0.029/12)^(12*9)
Simplifying the expression:
2,033.88 = P(1.002416667)^108
2,033.88 = P(1.343917334)
P = 2,033.88 / 1.343917334
P ≈ $1,511.29
Therefore, Francisco initially deposited approximately $1,511.29 into the savings account.
What is the sale price of a phone that was originally $199 but that has been marked down by 15 percent?
$159.15
$159.20
$169.10
$169.15
The final sale price of phone after mark-down of 15% is $169.15
What is selling price?
The selling price is defined as a price after the original price has been increased or decraesed.
Original price was $199.
Marked down 15% ==$199x 0.15 = $29.85
Final sale price after mark-down of 15% = $199 - $29.85 = $169.15
Hence, the final sale price of phone after mark-down of 15% is $169.15
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you deposited $100 into your bank account. the next day, you needed $ 20 to go mini golfing. represent this situation with a set of integers.
1.-$20
2.-$80
3. $20
4.$100
5. -$100
7j+5-8k
when j=0.5 and k=0.25
Answer:
6.5
Step-by-step explanation:
To perform this kind of exercise, it is necessary to replace the value indicated in each variable each time you find the variable in the equation.
[tex]7j+5-8k[/tex]
If j=0.5 and k=0.25, replace the value of each variable.
[tex]7(0.5)+5-8(0.25)=[/tex]
now perform the indicated operations
[tex]7(0.5)+5-8(0.25)=3.5+5-2=6.5[/tex]
Answer:
6.5
Step-by-step explanation:
an airport offers three shuttles that run on different schedules. if all shuttles leave the airport at 4:00P.M., at what time will they next leave the airport together? a leaves every 8 mins, b every 10 mins and c every 12 mins. When is the next time they will all leave together
What is the smallest angle of rotational symmetry that maps a regular pentagon onto itself?
Enter your answer in the box.
___°
Answer:
72º
Step-by-step explanation:
In order to calculate this you have to remember that the center angle of any polygon measures 360º, so what we do is just divide those 360 by the number of angles that you will find in the polygon, the number of angles equals the number of sides, so the pentagon has 5 sides, it will also have 5 angles. So we just divide the 360/5=72
So the smallest angle of rotational symmetry that maps a regular pentagon onto itself will be 72º
Suppose candidate a for a town council seat receives 43% of the votes in an election. as voters leave the polls they are asked who they voted for. what is the probability that less than 40% of the 80 voters surveyed indicate they voted for candidate a? assume an infinite population.
The probability that less than 40% of the 80 voters surveyed indicate they voted for candidate A is P(phat <0.4) = P((phat-p)/sqrt(p*(1-p)/n) <(0.4-0.43)/sqrt(0.43*(1-0.43)/80)) =P(Z<-0.542) =0.2939 (from standard normal table)
Answer:
29.46% probability that less than 40% of the 80 voters surveyed indicate they voted for candidate a
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
For a proportion p in a sample of size n, we have [tex]\mu = p, \sigma = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this problem, we have that:
[tex]\mu = 0.43, \sigma = \sqrt{\frac{0.43*0.57}{80}} = 0.05535[/tex]
What is the probability that less than 40% of the 80 voters surveyed indicate they voted for candidate a?
This is the pvalue of Z when X = 0.4. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.4 - 0.43}{0.05535}[/tex]
[tex]Z = -0.54[/tex]
[tex]Z = -0.54[/tex] has a pvalue of 0.2946
29.46% probability that less than 40% of the 80 voters surveyed indicate they voted for candidate a
Carly is 5 years younger then Lisa. Lisa is 3 times as old as Mark. What is a algebraic expression to represent Carly's age, in years if mark is m years old explain
Mark = m
Lisa = 3m ( 3 times as old as Mark)
Carly = 3m-5 ( 5 years younger than Lisa)
expression is C = 3m-5
solve 8y-3(4-2y)=6(y+1)
Sherri spent 4 hours exercising last week. If 5/6 of the time was spent jogging, how much time did she spend jogging?
What is $1000 for 6 years at 1.4% compounded semiannually?
Which sentence explains the correct first step in the solution of this equation?
4(x−3)=9
A. Add 2 to both sides.
B. Apply the distributive property to get 4x - 12 = 9.
C. Apply the distributive property to get 4x - 3 = 9.
D. Subtract 9 from both sides.
Answer:
b
Step-by-step explanation:
A 12 oz bottle of a new soda costs $2.49. What is the unit rate, rounded to the nearest tenth of a cent?
which comparison sentence best represents the equation 6 x 7=42? 7 is 6 times as many as 42? or 6 is 7 times as many as 42 or 42 is 6 times as many as 6 or 6 more than 7 is 42
The comparison sentence that best represents the equation 6 x 7 = 42 is option 3) 42 is 6 times as many as 7.
Let's break it down step-by-step:
Identify the numbers: 6, 7, and 42.Determine the relationship established by the equation: Multiplication.Apply the multiplication: 6 multiplied by 7 equals 42.Formulate the sentence based on this relationship: '42 is 6 times as many as 7.'Therefore, the correct choice is option 3) 42 is 6 times as many as 7.
35% of the students at Grandy High School are freshman. If there are 525 Freshman, how many students are not freshman?
Final answer:
To find the number of students who are not freshmen, we first calculate the total number of students using the percentage of freshmen and then subtract the number of freshmen from the total.
Explanation:
The student's question is asking for the total number of students at Grandy High School given that 35% of the students are freshmen and there are 525 freshmen. To find the total number of students, we can use the percentage formula:
Determine the percentage that the freshman represent: 35%.
Recognize that the 525 freshmen is 35% of the total. So, if 35% is 525, we can set up the equation: 0.35 × Total Number of Students = 525.
Divide both sides by 0.35 to find the total number of students: Total Number of Students = 525 ÷ 0.35.
Calculate the total number of students: Total Number of Students = 1500.
Since 35% are freshmen, the remaining 65% are not freshmen. Now, calculate 65% of the total students: 0.65 × 1500 = 975.
Therefore, 975 students are not freshmen.
Solve the inequality for x. Show each step of the solution. 12 x>9(2x-3)-15 (I'm having trouble with this one spefically)
if <PQR is vertical to <RQS and M<RQS=36 degrees,what is the measure of <PQR?
Twelve of the students in the school choir like to sing solos. These 12 students make up 24% of the choir. How many students are in the choir?
Answer:
The answer is 50 students
Step-by-step explanation:
Jess spent 7x minutes on the computer. Her sister spent 5 x + 10 minutes on the computer, which was the same amount of time Jess spent. How many minutes was Jess on the computer?
Answer: 35 minutes
Step-by-step explanation:
Given : Jess spent 7x minutes on the computer.
Her sister spent 5 x + 10 minutes on the computer, which was the same amount of time Jess spent.
Thus , we have
[tex]7x=5x+10[/tex]
Subtract 5x from both the sides , we get
[tex]2x=10[/tex]
Divide both sides by 2, we get
[tex]x=5[/tex]
Now, the time spent by Jess = 7(5)=35 minutes
Hence, Jess was 35 minutes on computer.
which expression represents the perimeter of a rectangle above? the width is (3y-5)ft and the length is 2yft
a. (5y-5)
b. (10y+10)
c. (10y-10
d. (6y^2-10y)
The perimeter of a rectangle is 10(y-1).
Option (c) is correct.
It is required to find the expression of perimeter of a rectangle.
What is rectangle?A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees.
Given that:
Let the length of rectangle be 3y-5
Let the breadth of rectangle be 2y
As we know the formula for perimeter,
So,
Perimeter (P)= 2Length (L) +2Width (W)
P=2L + 2W
P=2(2y)+2(3y-5)
P=4y+6y-10
P=10y-10
∴P=10(y-1)
Therefore, the perimeter of a rectangle is 10(y-1).
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there are 7 days in 1 week. some months consist of 30 days. how manu weeks are there in 280 days
There are a total of 40 weeks in 280 days.
What is Division?Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Given that there are 7 days in 1 week and some months consist of 30 days. Now, the number of weeks that 280 days will have can be found as,
Number of weeks = Total number of days / Number of days in a week
= 280 days / 7 days per week
= 40 week
Therefore, There are 40 weeks in 280 days.
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Using the information from problem #1, if a 32 inch Northern Pike is caught, then the weight in pounds as predicted by the least-squares line is ____ pounds. (Round your answer to 2 decimal places).
Draw a model to represent the problem 6/12 divided by 1/4
If charlene brewster has times of 8.4, 8.6, 8.3, 8.5, 8.7 ans 8.5 and a performance rating of 110% percent, what is the normal time for this operation? is she faster or slower then normal?
The normal time for this operation is approximately 8.333 seconds. Charlene Brewster is performing at a similar speed to the average for this operation.
Explanation:The question provides the lap times for Charlene Brewster as 8.4, 8.6, 8.3, 8.5, 8.7, and 8.5, with a performance rating of 110%. To find the normal time for this operation, we can calculate the average of the lap times. Adding all the lap times together and dividing by the number of laps, we get (8.4 + 8.6 + 8.3 + 8.5 + 8.7 + 8.5) / 6 = 50 / 6 = 8.333. Therefore, the normal time for this operation is approximately 8.333 seconds.
Comparing the normal time to Charlene's lap times, we see that her lap times are relatively close to the normal time. This indicates that she is performing at a similar speed to the average for this operation.
The height of a grain of a cylindrical silo is is increasing at a constant rate of 4 feet per minute At what rate is the volume of grain in the cylinder if the radius of the silo is 10 feet?
Just need the set up of the derivative